How Does Poiseuille's Law Calculate Blood Flow Speed in the Pulmonary Artery?

[je55ica7]

The pulmonary artery, which connects the heart to the lungs, has an inner radius of 2.8 mm and is 8.5 cm long. If the pressure drop between the heart and lungs is 400 Pa, what is the average speed of blood in the pulmonary artery?

I am using the equation pi*r^4(p1-p2)/(8*viscosity*length)

Would the p1-p2 be -400N or 400N? I thought a speed couldn't be negative... but it says "pressure drop". Would the answer be in m/s?

I'm lost.

 

[mcah5]

It depends on which way you choose to be positive, and which way to be negative. If you choose from the heart to the lungs to be positive, the p1-p2 = 400 where p1 is the pressure at the heart and p2 is the pressure at the lungs. Then your flow rate would be positive. You could also choose from the lungs to the heart to be positive, and in that case p1 is the pressure at the lungs and p2 is the pressure at the heart, so p1-p2 = -400. Then your flowrate would be negative.

 

[quicknote]

The pressure drop in this case refers to the difference in pressure between the heart and lungs, so it would be 400 Pa. This value should be positive since it is a difference in pressure, not a specific pressure value.

In terms of the units for the answer, it would depend on the units used for the other variables in the equation. The radius is given in millimeters and the length is given in centimeters, so the units for viscosity would also need to be converted to match. The final answer would be in a unit of velocity, such as meters per second.

It is important to note that this equation is a simplified version of Poiseuille's Law and does not take into account factors such as the pulsatile nature of blood flow and the changing cross-sectional area of the artery. Therefore, the calculated average speed may not be an accurate representation of the actual speed of blood flow in the pulmonary artery.